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The medicinal thermometer commonly used in homes can be read \(\pm 0.1^{\circ} \mathrm{F}\), whereas those in the doctor"s office may be accurate to \(\pm 0.1^{\circ} \mathrm{C}\). In degrees Celsius, express the percent error expected from each of these thermometers in measuring a person's body temperature of \(38.9^{\circ} \mathrm{C}\).

Short Answer

Expert verified
The percent error for the home thermometer is -45.5% and for the doctor's thermometer is 0.26% in Celsius.

Step by step solution

01

Understand and convert Fahrenheit to Celsius

First, in order to make comparisons between the readings of home and doctor's thermometers, the error in Fahrenheit needs to be converted to Celsius. The formula to convert Fahrenheit to Celsius is \((F - 32)/1.8 = C\). Thus, the error in temperature measured at home is \(((0.1 - 32) / 1.8) = -17.72^{\circ}C\)
02

Calculate the percent error

The percent error for a reading is defined as the absolute value of the error divided by the actual value, then multiplied by 100. In this case, the actual temperature is 38.9°C. Thus, the percent errors for the home and doctor's thermometers are \(\frac{-17.72}{38.9} * 100 = -45.5%\), and \(\frac{0.1}{38.9} * 100 = 0.26%\), respectively.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Fahrenheit to Celsius Conversion
Understanding the conversion from Fahrenheit to Celsius is vital for interpreting temperature measurements across different regions and industries. The key formula to remember is \( (F - 32) / 1.8 = C \) where \( F \) is the temperature in degrees Fahrenheit and \( C \) is the temperature in degrees Celsius.

To illustrate, a change of \(1^\circ F\) is not equivalent to a change of \(1^\circ C\); in fact, a change of \(1^\circ F\) is approximately equal to a change of \(0.56^\circ C\). This is because the two scales have different zero points and increments per degree. Being able to convert these measurements correctly ensures accuracy in scientific calculations and everyday life. When it comes to error calculation, it's crucial to apply this conversion to maintain consistency within the measurement system being used.
Thermometer Accuracy
When measuring temperature, the accuracy of the thermometer is as crucial as the measurement itself. The term 'accuracy' refers to how close the measured value is to the actual temperature. Thermometers often come with an accuracy range, such as \( \pm 0.1^\circ F \) or \( \pm 0.1^\circ C \).

For instance, a medicinal thermometer used at home with a \( \pm 0.1^\circ F \) accuracy implies that the actual temperature could be \(0.1^\circ F\) higher or lower than the displayed reading. Comparatively, professional-grade thermometers, like those used in a doctor's office, might have better accuracy, which is critical in situations where precise temperature measurements are needed for diagnosis or treatment decisions. Understanding the accuracy range helps interpret the reliability of temperature readings and is particularly relevant for converting and comparing values between different measurement units.
Temperature Measurement in Chemistry
In the field of chemistry, temperature measurement is not just a routine process; it is a cornerstone for experimental accuracy. Chemical reactions are often highly sensitive to temperature, and even small variances can lead to different outcomes. Therefore, understanding the concept of percent error in temperature readings is essential for chemists.

The percent error provides information on the reliability of the measurement relative to the actual temperature. It is calculated by taking the absolute value of the difference between the measured value and the true value, divided by the true value, and then multiplied by 100 to obtain a percentage. This figure is used to assess the precision of a measurement, and by comparing the percent errors of different thermometers, chemists can determine which device is most suitable for their experiments, ultimately ensuring the validity and reproducibility of their results.

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Most popular questions from this chapter

Describe the three temperature scales used in the laboratory and in everyday life: the Fahrenheit scale, the Celsius scale, and the Kelvin scale.

Calculate the mass of each of the following: (a) a sphere of gold with a radius of \(10.0 \mathrm{~cm}\) [ the volume of a sphere with a radius \(r\) is \(V=(4 / 3) \pi r^{3} ;\) the density of gold \(\left.=19.3 \mathrm{~g} / \mathrm{cm}^{3}\right],\) (b) a cube of platinum of edge length \(0.040 \mathrm{~mm}\) (the density of platinum \(=\) \(\left.21.4 \mathrm{~g} / \mathrm{cm}^{3}\right),\) (c) \(50.0 \mathrm{~mL}\) of ethanol (the density of cthanol \(=0.798 \mathrm{~g} / \mathrm{mL}\) ).

Chlorine is used to disinfect swimming pools. The accepted concentration for this purpose is 1 ppm chlorine, or \(1 \mathrm{~g}\) of chlorine per million grams of water. Calculate the volume of a chlorine solution (in milliliters) a homeowner should add to her swimming pool if the solution contains 6.0 percent chlorine by mass and there are \(2.0 \times 10^{4}\) gallons of water in the pool. ( 1 gallon \(=3.79 \mathrm{~L} ;\) density of liquids $=1.0 \mathrm{~g} / \mathrm{mL} .

Suppose that a new temperature scale has been devised on which the melting point of ethanol \(\left(-117.3^{\circ} \mathrm{C}\right)\) and the boiling point of ethanol \(\left(78.3^{\circ} \mathrm{C}\right)\) are taken as \(0^{\circ} \mathrm{S}\) and \(100^{\circ} \mathrm{S},\) respectively where \(S\) is the symbol for the new temperature scale. Derive an equation relating a reading on this scale to a reading on the Celsius scale. What would this thermometer read at \(25^{\circ} \mathrm{C}\) ?

The circumference of an NBA-approved basketball is 29.6 in. Given that the radius of Earth is about \(6400 \mathrm{~km},\) how many basketballs would it take to circle around the equator with the basketballs touching one another? Round off your answer to an integer with three significant figures.

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